Let's break this problem down into parts step by step.
Part 1: Evaluate the first expression
[
\frac{9.2 \times 6.4 \times 0.15}{1.6 \times 4.6 \times 0.03}
]
Calculate the numerator:
- ( 9.2 \times 6.4 = 58.88 )
- ( 58.88 \times 0.15 = 8.832 )
Calculate the denominator:
- ( 1.6 \times 4.6 = 7.36 )
- ( 7.36 \times 0.03 = 0.2208 )
Now, substitute these values into the expression:
[
\frac{8.832}{0.2208} \approx 40
]
Part 2: Evaluate the second expression
This expression is:
[
\frac{4}{5} \times \frac{3}{5} + 2 \div \frac{8}{5}
]
Calculate (\frac{4}{5} \times \frac{3}{5}):
[
\frac{4 \times 3}{5 \times 5} = \frac{12}{25}
]
Calculate (2 \div \frac{8}{5}):
[
2 \times \frac{5}{8} = \frac{10}{8} = \frac{5}{4}
]
Now add them up:
To add (\frac{12}{25}) and (\frac{5}{4}), convert (\frac{5}{4}) to have a common denominator with (\frac{12}{25}).
The least common multiple of 25 and 4 is 100.
- (\frac{12}{25} = \frac{12 \times 4}{25 \times 4} = \frac{48}{100})
- (\frac{5}{4} = \frac{5 \times 25}{4 \times 25} = \frac{125}{100})
Now, adding them:
[
\frac{48}{100} + \frac{125}{100} = \frac{173}{100} = 1.73
]
Part 3: Evaluate the final expression
The final expression is:
[
0.18 \div 1.5 + 2.88
]
Calculate (0.18 \div 1.5):
[
0.18 \div 1.5 = \frac{0.18}{1.5} = \frac{18}{150} = \frac{3}{25} = 0.12
]
Now add (0.12) to (2.88):
[
0.12 + 2.88 = 3.00
]
Final Answers:
- The first expression evaluates to approximately (40).
- The second expression evaluates to (1.73).
- The final expression evaluates to (3.00).
